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LHC Radio Frequency Swing

LHC Radio Frequency Swing . P. Baudrenghien AB/RF. Frequency Program for Synchrotrons. B is the guide field in T: 0.539 T to 8.386 T f inf = 400.789 662 MHz with h =35640 and 2 p R =26658.883m r is the bending radius r = 2784.32 m

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LHC Radio Frequency Swing

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  1. LHC Radio Frequency Swing P. Baudrenghien AB/RF

  2. Frequency Program for Synchrotrons B is the guide field in T: 0.539 T to 8.386 T finf = 400.789 662 MHz with h=35640 and 2pR=26658.883m ris the bending radiusr = 2784.32 m E0 is the rest energy of the particle/ion being accelerated (in eV) q is the number of elementary charges in the particle/ion LHC conceptual design 1995 LEADE meeting

  3. Proton acceleration We have: E0 = 938.26 x106 eV q = 1 The RF frequency ramps from 400.788 790 MHz at injection (0.539 T) to 400.789 658 MHz at top energy (8.386 T) N.B.: The bunch frequency @ 40 MHz is 1/10 times the above RF frequency. LEADE meeting

  4. Ions Acceleration E0 = rest energy of ion = sum of energy of protons, neutrons (and electrons) minus binding energy q = number of protons (minus number of electrons) In all cases E0/q will be larger than the case of proton. Ions are less relativistic at injection and the frequency swing is larger. LEADE meeting

  5. Lead ion acceleration For fully stripped lead Pb20882+we have: q = 82 (82 protons) E0 = 193.683 956 GeV considering the 82 p and 126 n with mp = 938.259 MeV, mn= 939.553 MeV and a binding energy of 7.87 MeV/nucleon E0/q= 2.362 x109 (to be compared to 0.93826 x 109 for protons) The RF frequency ramps from 400.784 139 MHz at injection (0.539 T) to 400.789 639 MHz at top energy (8.386 T) LEADE meeting

  6. Other ions ? Considering only fully stripped ions: • for In11549+we getE0 = 107.08 GeV and E0/q= 2.185 x109 • for Kr8436+we getE0 = 78.215 GeV and E0/q= 2.173 x109 • for Ar4018+we getE0 = 37.24 GeV and E0/q= 2.069 x109 • for Sn12050+we getE0 = 111.74 GeV and E0/q= 2.235 x109 • for O168+we getE0 = 14.90 GeV and E0/q= 1.862 x109 In all cases the frequency swing is smaller than withPb20882+ (E0/q= 2.362 x109) N.B.: The above figures for E0 are approximations using the 7.87 MeV/nucleon figure for binding energy. Exact for Pb only. LEADE meeting

  7. Remarks • In theory the frequency swing is not relevant to the experiment since you are only concerned by the RF during collisions • We do not guarantee any meaningful RF when no beam is in the machine (degaussing, access, shutdown,…) LEADE meeting

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